Problem: What do the following two equations represent? $-2x-3y = -5$ $15x-10y = -3$
Solution: Putting the first equation in $y = mx + b$ form gives: $-2x-3y = -5$ $-3y = 2x-5$ $y = -\dfrac{2}{3}x + \dfrac{5}{3}$ Putting the second equation in $y = mx + b$ form gives: $15x-10y = -3$ $-10y = -15x-3$ $y = \dfrac{3}{2}x + \dfrac{3}{10}$ The slopes are negative inverses of each other, so the lines are perpendicular.